Efficient resource allocation under multi-unit demand

We study resource allocation with multi-unit demand, such as the allocation of courses to students. In contrast to the case of single-unit demand, no stable mechanism, not even the (student-proposing) deferred acceptance algorithm, achieves desirable properties: it is not strategy-proof and the resulting allocation is not even weakly efficient under submitted preferences. We characterize the priority structure of courses over students under which stability is consistent with strategy-proofness or efficiency. We show that stability is compatible with strategy-proofness or efficiency if and only if the priority structure is essentially homogeneous. This result suggests that efficient allocation under multi-unit demand is difficult and that the use of stable mechanisms may not deliver desirable outcomes.